Eigenvector calculation

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Kamuran
Kamuran 2011-1-24
编辑： Naveed Ahmed 2023-10-24
I am trying to calculate the eigenvectors and eigenvalues for the following matrix (6,6) and I am getting complex eigenvector which I should not. I check the eigenvectors with maple and no complex eigenvector. Can anyone help me? ( complex numbers are not small. There on the same order or real ones)
-30.400000000000009 20.099689437998496 16.988854381999836 -12.099689437998487 13.411145618000168 -7.999999999999998
-1.105572809000086 -3.811145618000166 4.683281572999748 1.105572809000084 -3.577708763999662 2.705572809000083
4.494427190999916 -0.683281572999748 -7.388854381999832 3.577708763999663 2.894427190999915 -2.894427190999915
-2.894427190999916 2.894427190999916 3.577708763999664 -7.388854381999831 -0.683281572999745 4.494427190999913
2.705572809000084 -3.577708763999665 1.105572809000085 4.683281572999745 -3.811145618000171 -1.105572809000080
-7.999999999999998 13.411145618000166 -12.099689437998482 16.988854381999822 20.099689437998467 -30.399999999999970
You can see that the first 3 row almost a mirror image of last 3 (or vice versa). Actually it has to be to same, but due to around offs coming from calculation creates 10^-13 differences. If I make those changes and makes them excatly mirror images no complex eigenvectors (which is little odd)
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Naveed Ahmed
Naveed Ahmed 2023-7-31
编辑：Naveed Ahmed 2023-10-24
and the matrix should always be 'Square' to get the eigean vectors.
Torsten
Torsten 2023-7-31
@Naveed Ahmed
How should A*x = lambda*x hold if A were not square ?

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Ned Gulley
Ned Gulley 2011-1-25
When I run the eig command (see help here: eig) I don't get any complex eigenvectors. Maybe the problem is data entry?
Assuming your matrix is in a, then
[v,d] = eig(a)
v =
-0.7059 -0.6622 0.4830 0.3203 -0.0000 0.4644
0.0294 -0.1076 0.4654 -0.4804 0.5774 0.4425
0.0294 0.2235 0.2239 0.3203 -0.0000 -0.2974
0.0294 -0.2235 -0.2239 -0.4804 0.5774 -0.2974
0.0294 0.1076 -0.4654 0.3203 -0.0000 0.4425
-0.7059 0.6622 -0.4830 -0.4804 0.5774 0.4644
d =
-40.0000 0 0 0 0 0
0 -31.1332 0 0 0 0
0 0 -2.4668 0 0 0
0 0 0 0.0000 0 0
0 0 0 0 -0.0000 0
0 0 0 0 0 -9.6000
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Bruno Luong
Bruno Luong 2011-1-25
You might try free host servers, but as I have pointed out earlier, the smallest eigen values are 1e-17 of the largest, so any small perturbation of matrix elements could easily make smallest eigen value becomes complex. That's not a surprise to me. You might need to make some safeguard code against this issue.
Christine Tobler
Christine Tobler 2023-7-31
Yes, you can attach a .mat file (look for the little "attachment button" when editing the post - like a paperclip).
For this small matrix, here's a way you can display it so that there are no differences:
for ii=1:size(A, 1)
s(ii) = string(sprintf('%.20e ', A(ii, :)));
end
disp("Acopy = [" + join(s, ";"+newline) + "]")
Run this code where you have the original matrix A, then use isequal(A, Acopy) to verify it matches exactly.

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